Some numbers

N[Log[10,2],10]

Log[2,10]//N

Podgson’s ratio

pr=(100^(1/5))

N[pr]

Log[pr,x]

(5/2)Log[10,x]==Log[pr,x]

(b^(Log[b,y]))

Assuming[
b>0&&x∈Reals,
Log[b,(b^x)]//Simplify
]

(1/(Sin[x]))